Final answer:
The statement (2+1)+9=2+(1+9) demonstrates the Associative Property of Addition, which states that the grouping of numbers in an addition does not affect the sum.
Step-by-step explanation:
The equation (2+1)+9=2+(1+9) is an example of the Associative Property of Addition. This property states that when adding three or more numbers, the way in which the numbers are grouped does not change the sum. In other words, the parentheses indicating the order of operation can be moved without changing the result of the addition. For example, (2+1)+9 can be regrouped to 2+(1+9), and it will still equal 12.
The Commutative Property of Addition states that the order of the numbers does not affect the sum; for example, 2+3 is the same as 3+2. The Commutative Property of Multiplication similarly indicates that the order of factors does not affect the product, as in 2x3 equals 3x2. These properties allow for flexibility in calculations.
Lastly, the Associative Property of Multiplication states that the grouping of factors does not affect the product, just like the associative property of addition. And the Distributive Property shows how a number can be distributed across a sum within parentheses, exemplified in a(b+c) = ab + ac.